
Re: Circlecircle tangent puzzle
Posted:
Jun 15, 2012 11:53 AM


> Let A, B be the centers of two circles with radius > r1, r2 respectively, where r1r2 is very small. > Construct the exterior tangent to the given circles. > > In this puzzle is sought a practical construction on an A4 sheet of paper that avoids entirely the use of r1r2.
Let AA0 be the radius of (A,r1) perpendicular to line AB Let BB0 be the radius of (B,r2) perpendicular to line AB From A drop perp AA1 to line A0B0 From B drop perp BB1 to line A0B0 Produce AA1 to meet circle(A,r1) in A12 Produce BB1 to meet circle(B,r2) in B12
Line A12B12 is a close approx to the required tangent.
A second iteration, by dropping perps from A and B to line A12B12 and extending these to A22B22 will be only marginally more accurate for the tangent line, but it will give a slight improvement of the location of the points of tangency.
Regards, Peter Scales.

